R. Zander

Free Planar Motion of Flexible Beams in MBS – A Comparison of Models #

Abstract Two approaches for the description of free planar motion of elastic beam structures are studied: a method using redundant coordinate sets to maintain a moving frame of reference (MFR) discretization in a finite element formulation and the absolute nodal coordinate formulation (ANCF). Both are treated within the modern framework for multi-body systems including bi- and unilateral constraints as well as non-smooth dynamics. Numerical efficiency and accuracy of the models are investigated using two examples: A slider-crank mechanism with a flexible beam is used to study computational cost and the convergence for finer spatial discretizations. Non-smooth dynamics is studied for an elastic rocking rod built of an elastic beam bouncing on two fixed point obstacles.

Impacts on Beam Structures: Interactions of Wave Propagation and Global Dynamics

The paper investigates the interactions between impacting rigid bodies and the induced elastic waves in planar beam structures. Therefor, the framework for non-smooth dynamics of multibody systems including elastic impacts is applicated to a finite element description for beams in free planar motion. The model is used for two numerical examples: a cantilever beam with multiple impacts to several point masses and an elastic model of the rocking rod, which is used to adapt the restitution coefficient for a rigid model.

Non-Smooth Flexible Multi-Body Systems With Non-Primitive Contours

This article shows the formulation of flexible multi-body systems for contact dynamics. A short introduction is given on the mathematical formulation of non-smooth multi-body systems, which are marked by jumps within the system velocities. The paper focuses on the geometrical description of flexible components: these can be modeled directly in the system or gained from external pre-processes like for example finite element codes. Since the contact algorithms require contour information, the body shapes need to be interpolated independent from the description used for dynamics within external codes. The interpolation can respond especially on the requirements of contact simulations. Discrete nodes of the external mesh are used as reference and interface for contacts. Two examples show the potential of the formulations: an eccentrically excited machine on elastic ground and a bunch of dice falling into an elastic basin.Copyright

Controller Design for a Rubbing Rotor

A new approach to control a rubbing rotor by applying an active auxiliary bearing is developed. The auxiliary bearing is attached to the foundation via two unidirectional actuators. The control force is applied indirectly using the active auxiliary bearing only in case of rubbing. A framework for the development of a feedback controller for an active auxiliary bearing is presented. The theory of a robust two-phase control strategy which guarantees a smooth transition from free rotor motion to the state of full annular rub is presented. A simulation environment for the elastic rotor and the auxiliary bearing including the non-smooth nonlinear dynamics of the rubbing contact is used to develop the feedback controller. Experimental studies have been carried out at a rotor test rig. Various experiments show the outstanding success of the strategy. In case of rubbing, the contact forces are reduced up to 90%.